Coordinates Converter
Convert latitude and longitude to degrees, minutes and seconds, and to UTM zone, easting and northing.
What it does
Almost every piece of digital mapping works in decimal degrees, while charts, aerial photographs and a lot of field equipment work in degrees, minutes and seconds. The conversion is simple: the part after the decimal point is a fraction of a degree, and a degree is 60 minutes and a minute is 60 seconds.
The other half of the answer is the grid reference. The Universal Transverse Mercator system cuts the world into sixty zones, each six degrees of longitude wide, and gives a point an easting and a northing measured in metres from a central meridian and from the equator. The zone number comes straight from the longitude, with a central meridian six degrees west of the middle of the zone.
The projection is the part that needs care. The US Geological Survey working manual, the standard reference on map projections, gives the ellipsoidal transverse Mercator series used here, along with the scale factor of 0.9996 and the false easting of 500,000 metres. NOAA's datum tables give the WGS 84 ellipsoid, with a semi major axis of 6,378,137 metres and a flattening of 1 in 298.257223563.
Two regions break the regular six degree pattern. Southern Norway, between 56 and 64 degrees north and 3 to 12 degrees east, is widened into zone 32, and Svalbard, north of 72 degrees, has its zones widened to 31, 33, 35 and 37. The zone rules for those exceptions are set out in the geographic coordinate system references.
One warning about UTM. The numbers here are a projection, so they are only as good as the projection itself, which is a series rather than an exact solution. That is fine for the metre accuracy most work needs, and a surveyor working to the centimetre would use a national grid instead.
How to use
- Pick metric or imperial for the grid coordinates.
- Enter the latitude in decimal degrees, positive north.
- Enter the longitude in decimal degrees, positive east.
- Read the degrees, minutes and seconds form of both.
- Read the UTM zone, and check it against the zone you expected.
- Read the easting and northing, and remember they are metres on the WGS 84 ellipsoid.
Formula
- Latitude
- Angle north or south of the equator, in decimal degrees.
- Longitude
- Angle east or west of Greenwich, in decimal degrees.
- k0
- Scale factor of the transverse Mercator projection, 0.9996.
- a
- Semi major axis of the WGS 84 ellipsoid, 6,378,137 m.
- e2
- First eccentricity squared of the ellipsoid, used in the series.
The easting and northing are computed with the series printed in the USGS working manual, which is a finite approximation rather than the exact transverse Mercator solution, so the last metre or two can differ from a full projection library. The Norway exception applies to latitudes 56 to 64 degrees north, and the Svalbard exceptions to latitudes 72 to 84 degrees north.
Worked example
Example: 40.714722 north, 74.005972 west
Defaults: metric units with the latitude and longitude of lower Manhattan.
- Latitude: 0.714722 x 60 = 42.8833 minutes, and 0.8833 x 60 = 52.999 seconds, so 40 degrees 42 minutes 52.999 seconds north.
- Longitude: 0.005972 x 60 = 0.35832 minutes, and 0.35832 x 60 = 21.499 seconds, so 74 degrees 0 minutes 21.499 seconds west.
- Zone: floor((180 - 74.005972) / 6) + 1 = 18, with a central meridian at 75 degrees west.
- Easting: the series gives 583,959.3 m.
- Northing: the series gives 4,507,564.4 m.
- The tool shows 40 42' 52.999" N, 74 0' 21.499" W, 18N, 583,959.3 m and 4,507,564.4 m.
Reference table
| Place | Coordinates | Zone | Easting | Northing |
|---|---|---|---|---|
| Lower Manhattan | 40.714722 N, 74.005972 W | 18N | 583,959.3 m | 4,507,564.4 m |
| Null Island | 0, 0 | 31N | 166,021.4 m | 0.0 m |
| Central meridian | 0, 3 E | 31N | 500,000.0 m | 0.0 m |
| Oslo area | 60 N, 6 E | 32N | 332,705.2 m | 6,655,205.5 m |
| Sydney | 33.87 S, 151.21 E | 56S | 334,435.7 m | 6,250,816.4 m |
Limits
- Uses the transverse Mercator series, which is a finite approximation of the exact projection.
- Covers the UTM zones, which are defined for latitudes between 80 south and 84 north.
- Assumes the WGS 84 ellipsoid, so a point in another datum will be off by the difference between them.
- Does no datum transformation, so coordinates copied from an old map may need one before they line up.
Common mistakes
- Mixing the signs, so a western point comes out in the eastern hemisphere.
- Writing minutes and seconds as decimals, when 0.5 minutes is 30 seconds and not half a second.
- Forgetting the false northing, so a southern hemisphere point comes out with a negative northing.
- Using the zone number for the central meridian instead of the zone itself, which is one lower.
- Expecting the easting and northing to be exact, when they come from a series rather than the exact solution.
Try it yourself
Quick checks. Answers sit tucked under each question.
What is 40.714722 degrees north in degrees, minutes and seconds?
40 degrees 42 minutes 52.999 seconds north, because 0.714722 of a degree is 42.88332 minutes and the rest is 52.999 seconds.
Which UTM zone does a point at 74 degrees west sit in?
Zone 18, because floor((180 - 74) / 6) + 1 = 18, and its central meridian is 75 degrees west.
What are the UTM coordinates of the point 0, 0?
Zone 31N with an easting of 166,021.4 m and a northing of 0.0 m, because the central meridian of zone 31 is 3 degrees east, not 0.
Questions
How do I convert decimal degrees to degrees, minutes and seconds?
Take the whole degrees, multiply the decimal part by 60 for the minutes, and multiply the leftover decimal part by 60 for the seconds.
What is UTM?
The Universal Transverse Mercator system, which divides the world into sixty zones six degrees of longitude wide and gives every point an easting and a northing in metres.
Which datum does this use?
WGS 84, the same datum used by GPS, with a semi major axis of 6,378,137 metres and a flattening of 1 in 298.257223563.
Why is my northing negative in the southern hemisphere?
It should not be. The projection adds a false northing of 10,000,000 metres in the southern hemisphere so that every northing stays positive.
What is the wide zone 32?
An exception for southern Norway, where the six degree pattern would put the country in two zones. Zone 32 is widened to cover it, and Svalbard has a similar set of widened zones.
How accurate are the grid coordinates?
The series used here is accurate to within a metre or two over a single zone, which is fine for mapping and fieldwork. Survey work to the centimetre uses a national grid instead.
Sources
- US Geological Survey Professional Paper 1395: Map Projections, a working manual
- NOAA: vertical and horizontal datums, including WGS 84
- Apache Spatial Information System: geographic coordinate system references and UTM zone rules